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Energy release rate and stress intensity factors in planar elasticity in presence of smooth cracks

  • Stefano Almi
  • Ilaria Lucardesi
Article
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Abstract

In this work we first analyze the singular behavior of the displacement u of a linearly elastic body in dimension 2 close to the tip of a smooth crack, extending the well-known results for straight fractures to general smooth ones. As conjectured by Griffith (Phys Eng Sci 221:163–198, 1921), u behaves as the sum of an \(H^{2}\)-function and a linear combination of two singular functions whose profile is similar to the square root of the distance from the tip. The coefficients of the linear combination are the so called stress intensity factors. Afterwards, we prove the differentiability of the elastic energy with respect to an infinitesimal fracture elongation and we compute the energy release rate, enlightening its dependence on the stress intensity factors.

Keywords

Brittle fracture Stress intensity factor Energy release rate 

Mathematics Subject Classification

35Q74 35B40 74R10 74G40 74G70 

Notes

Acknowledgements

The work of the authors was partially supported by the European Research Council under Grant No. 501086 “High-Dimensional Sparse Optimal Control”. S.A. also acknowledges the support of the SFB TRR109.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.TU MünchenGarching bei MünchenGermany
  2. 2.Institut Élie Cartan de LorraineVandoeuvre-lès-NancyFrance

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